Exploring the boundary of quantum correlations with coherent light postprint

Abstract: Contextuality, a hallmark feature of the quantum theory, captures the incompatibility between quantum correlations and any noncontextual hidden-variable model. The Greenberger--Horne--Zeilinger (GHZ)-type paradoxes are proofs of contextuality which reveal this incompatibility with deterministic logical arguments. However, the simplest GHZ-type paradox with the fewest number of complete contexts and the largest degree of nonclassicality remains elusive. Here, we derive a GHZ-type paradox utilising only three complete contexts and show this number cannot be further reduced. We forward to demonstrating the paradox with an experiment which recovered all essential ingredients in a 37-dimensional contextuality test based on high-speed modulation, optical convolution and homodyne detection of time-multiplexed modes of coherent light that can be interpreted as a classical entity. By proposing and observing a strong form of contextuality in an extremely high-dimensional system, our results pave the way for the exploration of exotic quantum correlations with optical systems.